Implied volatility in option pricing is one of the most critical and yet least understood aspects of this business. Today's show focuses on options skew and the volatility smile for both inter-month and intra-month option contracts. Also, we'll talk very specifically about the impact of skew as expiration approaches and how Vega for near-term option contracts increases dramatically. This can make it seem like option skew is predicting a huge move right before expiration. But, is it really the case, and does this "predictive power" work in reality?

Introduction:

• We assume that the markets are not normally distributed and that there is an embedded skew.
• However, a normal distribution is a great learning tool for understanding options strategies. 
• When it comes to option pricing, there is a little put-side skew or negative skew that occurs. 
• This has to do with the concept that over time, more often than not, if a stock is going to go down, it will crash violently and fast. When the markets go up, they tend to float or naturally go up at a steady pace. 
• This is where the idea of volatility skew comes into play.

Volatility Skew

1. Volatility

• This is the actual implied volatility of option contracts.
• The embedded implied volatility that is present at any given time when we're looking at volatility skew
• What is the expectation of volatility for that contract for that strike price and expiration date in the future?

2. Skew

• Skew refers to the difference between one strike price and another or one expiration and another.
• Often people wrongly assume that "skew" means twisted or backward or like something went wrong — this is not the case.
• Skew refers to something asymmetric compared to some other strike price or expiration date
• Skew is the perceived risk of something happening on one side of the payoff diagram versus the other.
• Usually, we see this happen in equity index options because many institutions will use options as a hedging technique.

• Institutions will buy options contracts that are out-of-the-money on the put side, which then increases the price of the out-of-the-money put options. 
• However, it is too costly to buy them outright. So, they create a simple synthetic collar strategy by selling call options out-of-the-money to help finance that cost. 
• If they buy up the put options, then that buying increases the price of the put options. If they are selling call options, that is decreasing the price of the call options because of the selling pressure.
• This is naturally going to create some sort of skew in the pricing of those options contracts. 
• This skew, again, is on the put side.

Skew

1. Intra-month Skew

• This refers to the skew between individual strike prices in a single expiration month.

2. Inter-month Skew

• This looks at the volatility, generally, between the front-month expiration and a back-month expiration. 

• For example, when you get into an earnings event, the week that the earnings are announced, the weekly contracts' volatility goes through the roof. 
• Because the out-of-the-money call options are generally priced cheaper, and puts are generally priced a little bit more expensive, that's what creates a bit of this pricing skew. 
• Again, this is normal to have.

Inter-Month Skew

Example: SPY is trading at $280. Consider the August expiration SPY contracts that are $10 out on either end: the call options at $290 are priced at $15 while the $270 put options are trading at $85. This is a huge discrepancy in pricing, which shows the volatility skew in the market to the put side. As we go further and further out of the money on the put side, the option prices do not reduce their value as fast on the put side as on the call side.  

Looking at $5 increments between these two, the value of the $285 call options is $78. For the $290 call options, the price drops to $15. This is a pretty drastic and almost waterfall effect of option pricing as you go further out on the call side. Again, the reason for that is that markets generally do not have this crash up effect - they generally only float higher. 

On the put side, looking at the $275 put options, the price is $140. The price of the $270 put options is $85. It's not until you get all the way down to the $240 options on the put side that you find put options that are the same price as the $290 call options at $15. 

Intra-Month Skew

Example: Looking at the skew between August and September, we now start to see a little bit of that skew subside and maybe flatten out if you graph it. The skew between strikes as you go further out in time and the skew between option months starts to flatten out. You get a really high smile effect, but as you go further out in time, it tends to flatten out. At that point, there is so much time for the stock to move that we don't have as much skew. 

In this case, August expiration and September expiration have about a 2 point differential in volatility. The volatility expectation generally for August is about 12% volatility. The volatility expectation in September is about 14% volatility, but much flatter across all the different strike prices. You don't have the same dramatic waterfall effect on the call side as you go out to September expiration as you do with August expiration.

Volatility Smile

• Most people misunderstand what these volatility smile lines really represent when it comes to the differences between contract months: intra-month volatility smile. 

1. A Line that Resembles a Smile

2. The Skew

• People look at the volatility smile for expirations that are very close to expiration and see that the option prices are creating a smile effect, which means that the volatility that's baked into both the call side and the put side is very, very high. 
• This does not necessarily mean that those options contracts are a better deal.
• In fact, as we approach expiration, option Vega decreases because longer-dated option contracts are more tied to volatility changes.
• As we get closer to expiration, the impact of volatility on an option price goes down.
• A small change now could have a significant effect six months down the road.
• When you look at Vega as you're approaching expiration, it doesn't make that big of a difference in the overall trajectory.
• Later stage changes in volatility have a lower and lower impact on the option price.
• This means that the lower the Vega and the lower the option price, a much larger change in volatility is required to change that option price dramatically - a huge volatility event.
• Options contracts that are out of the money and close to expiration naturally have really high implied volatilities.
• This is not because the options contracts are insanely overpriced - it's just because they require a huge change in volatility to ever make any money.
• This is also why you see volatility on both ends of the spectrum for closer-dated option contracts.
• For weekly contracts, we see volatility really expand as we get out of the money.
• A 1% or 2% move can be made in a day or two on a weekly contract.
• But a multi-month move on a monthly or bi-monthly contract might mean that the stock floats higher and could crash lower at a much greater magnitude. That's why when you look at longer-dated option contracts, their volatility skew is much flatter.

How To Use Volatility Smile

• Understanding the impact of intra-month versus inter-month volatility is really important.
• If you understand how skew works and see that there is an enormous amount of put skew for a given expiration month, it means that those put options are much higher priced.
• So, selling puts or put spreads can be a little bit more profitable.
• You can also use it to realize how far to slide strike prices for a strangle

Example: If you set up a strangle $10 out on either end, you will naturally get some skew on the put side by selling the $10 out put options on SPY versus the $10 out call options. You can use Deltas as your proxy for where to set your strike prices. Deltas allow us to naturally account for skew in the market by selling the same Delta on either end of the stock. 

In the case of SPY for the August expiration contracts, if we were going to sell the 15 Delta options on either end, then we would be selling the $286 call options (stock trading around $280), and then the 15 Delta put options would be the $270's. Delta will naturally account for skew, making our put options a little bit further out and bring our call options in a little bit more.